Properties and Applications of Gromov Matrices In Network Inference

Abstract

In this paper, we review the commonly used breadth-first search (BFS) tree heuristic for network inference and estimation. The BFS method usually randomly chooses a BFS spanning tree in a graph to perform an estimation task. However, there are an intractable number of spanning trees in a dense graph. We represent a BFS tree with a Gromov matrix, and propose a method that constructs a parametric family of Gromov matrices for inference and estimation instead of a randomly selected BFS tree. This procedure increases the size of the candidate set and hence enhances the performance of the classical BFS heuristic. On the other hand, our new scheme is based on simple algebraic constructions using matrices, and hence is still computationally tractable. We discuss two applications on network inference and estimation to demonstrate the usefulness of the proposed method in handling signal and information over networks.